Cooperative behaviour among people facing social dilemmas remains an unsolved puzzle. Sanction systems such as punishment and reward are well-known solutions to social dilemmas. On the one hand, it is theorised that peer sanctions cannot maintain cooperation because of the intrusion of second-order free riders. On the other hand, experimental studies have widely reported that cooperation is sustainable by first-order sanction systems. To understand the divergence between theory and experimental results, we focus on the effects of beliefs about sanctions on promoting cooperation. While previous studies have revealed effects of beliefs about other people’s cooperation in public goods games (PGGs), the effect of beliefs about sanctions have not been considered. We conducted a scenario-based experiment using one-shot PGGs with and without sanction systems. The results revealed that beliefs about sanctions promote cooperation in a PGG when types of sanctions and some psychological attitudes to cooperation are controlled for. Our results indicate that the beliefs of actors promote cooperation despite the possible presence of second-order free riders. A belief about sanctions differs from a preference for cooperative behaviour and the amount a player pays to exercise a sanction. It is necessary to consider players’ beliefs about a sanction when studying its effectiveness.